Chapter 26: Q. 32 (page 738)

$50 p J$ of energy is stored in alocalid="1648664667304" $2.0 c m \times 2.0 \times 2.0 c m$ region of uniform electric field. What is the electric field strength?

Short Answer

Expert verified

The electric field strength is $1.19 \frac{k V}{m}$

Step by step solution

Step: 1 Given information

We have given that the $50 p J$ of energy in localid="1648663993355" $2.0 c m \times 2.0 c m \times 2.0 c m$ .

We need to find the electric field strength.

Step: 2 Simplify

The formula of energy as it relates to the strength of the electric field is

$u_{E} = \frac{1}{2} \in_{0} E^{2} (30.28)$

Considering the formula $u_{E_{}} = \frac{e n e r g y s t o r e d}{v o l u m e i n w h i c h i t i s s t o r e d}$ , meaning localid="1648664098321" $u_{E} = \frac{5 \times 10^{- 11} J}{{(0.020 c m)}^{3}} = 6.3 \times 10^{- 6 \frac{j}{m}}$ . The reader has not converted the initial units to base units; this solution omits changing $(p J)$ to $(J)$ and omits changing $(c m^{3})$ to $(m^{3})$ .

If we rearrange $(30.28)$ to solve for $E$

$u_{E} = \frac{1}{2} \in_{0} E^{2} \to 2 u_{E} = \in_{o} E^{2} \to \frac{2 u_{E}}{\in_{o}} = E^{2} \to E = \sqrt{\frac{2 u_{E}}{\in_{0}}}$

Using the numerical values of given variable and constant

localid="1648664073878" $E = \sqrt{\frac{2 u_{E}}{\in_{0}}} E = \sqrt{\frac{2 (6.3 \times 10^{- 6} \frac{j}{m})}{8.85 \times 10^{- 12} \frac{c^{2}}{N m^{2}}}} = 1.19 \times 10^{3} \frac{V}{m} = 1.19 k V / m$

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$50 p J$ of energy is stored in alocalid="1648664667304" $2.0 c m \times 2.0 \times 2.0 c m$ region of uniform electric field. What is the electric field strength?

Short Answer

Step by step solution

Step: 1 Given information

Step: 2 Simplify

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50pJof energy is stored in alocalid="1648664667304" 2.0cm×2.0×2.0cmregion of uniform electric field. What is the electric field strength?

Short Answer

Step by step solution

Step: 1 Given information

Step: 2 Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Fluids

Astrophysics

Quantum Physics

Engineering Physics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

$50 p J$ of energy is stored in alocalid="1648664667304" $2.0 c m \times 2.0 \times 2.0 c m$ region of uniform electric field. What is the electric field strength?